The processing of data gathered by frequency-scanning interferometers involves converting rates of interferometric variation accompanying variations in beam frequency into such length measures as surface topography or distance.
Frequency-scanning interferometers, also referred to as wavelength-scanning interferometers or multi-wavelength interferometers, derive from measures of interference taken at a succession of different beam frequencies (or wavelengths) path length differences between interfering object and reference beams. In contrast to conventional interferometers that compare path length differences between points within the same interference patterns and use additional interference patterns to resolve ambiguities of the intra-pattern comparisons, frequency-scanning interferometers resolve points within interference patterns individually, based upon interferometric (e.g., intensity or phase) fluctuations of corresponding points within different interference patterns produced at different beam frequencies.
As such, a wider range of surface roughness and distances can be unambiguously measured by frequency-scanning interferometers. Conventional interferometers are typically limited to measuring step sizes in the direction of illumination within the fringe spacing of their interference patterns, which correspond to the wavelength of the illumination. The measurement of such step sizes by frequency-scanning interferometers is independent of the nominal wavelength of illumination, depending instead on the average interval between the beam frequencies. The finer the interval, the larger the range of unambiguous measurement. Thus, frequency-scanning interferometers can provide measures of rough or diffuse surfaces at beam frequencies that produce speckle-ridden interference patterns unintelligible to conventional interferometers.
Frequency-scanning interferometers are especially useful for measuring surface profiles of test objects as measures of surface variations taken normal to a reference plane or surface. Recent developments of frequency-scanning interferometry include the use of components such as tunable diode lasers and CCD detector arrays. As a result, compact, accurate, and fast systems have been developed, which have the capability of performing measurements for both imaging and non-imaging applications.
A known type of frequency-scanning interferometer system 10 is depicted in FIG. 1. While in the overall form of a Twyman-Green interferometer, a tunable laser 12 under the control of a computer 14 produces a measuring beam 16 that can be tuned through a range of different frequencies. Beam conditioning optics 18 expand and collimate the measuring beam 16. A folding mirror 20 directs the measuring beam 16 to a beamsplitter 22 that divides the measuring beam 16 into a object beam 24 and a reference beam 26. The object beam 24 retroreflects from a test object 30, and the reference beam 26 retroreflects from a reference mirror 32. The beamsplitter 22 recombines the object beam 24 and the reference beam 26, and imaging optics 34 (such as a lens or group of lenses) focus overlapping images of the test object 30 and the reference mirror 32 onto a detector array 36 (such as a CCD array of elements). The detector array 36 records the interferometric values of an interference pattern produced by path length variations between the object and reference beams. 24 and 26. Outputs from the detector array 36 are stored and processed in the computer 14.
The elements of the detector array 36 record local interferometric values subject to the interference between the object and reference beams 24 and 26. Each of the interferometric values is traceable to a spot on the test object 30. However, instead of comparing interferometric values between the array elements to determine phase differences between the object and reference beams 24 and 26 throughout an interference pattern as a primary measure of surface variation, a set of additional interference patterns is recorded for a series of different beam frequencies (or wavelengths) of the measuring beam 16. The tunable laser 12 is stepped through a succession of incrementally varying beam frequencies, and the detector array 36 records the corresponding interference patterns. Data frames recording individual interference patterns numbering 16 or 32 frames are typical.
The local interferometric values vary in a sinusoidal manner with changes in beam frequency, cycling between conditions of constructive and destructive interference. The rate of interferometric variation, e.g., the frequency of intensity variation, is a function of the path length differences between the local portions of the object and reference beams 24 and 26. Gradual changes in intensity (lower interference frequency variation) occur at small path length differences, and more rapid changes in intensity (higher interference frequency variation) occur at large path length differences.
Discrete Fourier transforms can be used within the computer 14 to identify the interference frequencies of interferometric (e.g., intensity) variation accompanying the incremental changes in the beam frequency of the measuring beam 16. The computer 14 also converts the interference frequencies of interferometric variation into measures of local path length differences between the object and reference beams 24 and 26, which can be used to construct a three-dimensional image of the test object 30 as measures of profile variations from a surface of the reference mirror 32. Since the reference mirror 32 is planar, the determined optical path differences are equivalent to deviations of the object 30 from a plane. The resulting three-dimensional topographical information can be further processed to measure important characteristics of the object 30 (e.g. flatness or parallelism), which are useful for quality control of precision manufactured parts.
Considerable computational time is required for computing the Fourier transforms for each of a number of points sampled from the interference patterns. For example, intensity detector arrays having a matrix of one thousand by one thousand detector elements require up to one million Fourier transforms to be performed. The computing time for each Fourier transform increases with both the number of different interference patterns recorded and the number of Fourier frequency samples tested. The range of detectable interference frequencies is dependent upon the number of recorded interference patterns, and the accuracy with which the interference frequencies can be identified depends upon the number of Fourier frequency samples used. Accordingly, computing time, which is affected by multiple dimensions, can slow measurement procedures, rendering the measurement procedures too slow for xe2x80x9creal timexe2x80x9d or xe2x80x9cinlinexe2x80x9d inspections.
Significant reductions in computational time are made for processing interferometric data produced by frequency-scanning interferometers. Improvements are made to both simplify and streamline processing. Faster measurements and measurements with higher accuracy are possible.
One object of the invention is to provide an improved frequency-scanning interferometry system for distance or range measurement, including such systems that produce 3-D images of the surface profile of a test object, wherein computations of distance or range values are carried out with speed and accuracy. A more general object of the invention is to provide an improved system for deriving distance or range measurements from interferometric data.
The invention can be practiced as a multi-stage process for interpreting interferometric fluctuations of frequency-scanning interferometers. A succession of N interference patterns are produced between object and reference beams at N different beam frequencies within a range of beam frequencies. Interferometric data is recorded for a corresponding area appearing in each of the N interference patterns. The interferometric data for the corresponding area cycles through conditions of constructive and destructive interference with variation in the beam frequencies. A first approximation is made of an interference frequency corresponding to the number of interference cycles the interferometric data for the corresponding area undergoes throughout the range of beam frequencies. The bounds of this first approximation are determined. A second approximation is made of the interference frequency within the bounds of the first approximation of the interference frequency. The second or higher approximation of the interference frequency is then converted into a measure corresponding to a path length difference between portions of the object and reference beams that interfere within the corresponding area of the interference patterns.
The first approximation preferably approximates the interference frequency from among the number N or less choices of interference frequency. In particular, the first approximation preferably approximates the interference frequency from among approximately N/2 choices of interference frequency. As such, the choices of interference frequency within the first approximation are distinguished by approximately whole cycles of constructive and destructive interference within the range of beam frequencies. The choices of interference frequency within the second approximation are distinguished by significantly less than whole cycles of constructive and destructive interference within the range of beam frequencies.
Preferably, the first approximation approximates the interference frequency from among a first range of interference frequencies separated by a first increment, the second approximation approximates the interference frequency from among a second range of interference frequencies separated by a second increment, and the second range of frequencies is approximately equal to the first increment separating interference frequencies within the first range.
Also preferably, the first approximation approximates the interference frequency from among M1 choices of interference frequency, and the second approximation approximates the interference frequency from among M2 choices of interference frequency. The second approximation is substantially equivalent in accuracy to single approximation that approximates the interference frequency from among the product of M1 times M2 choices of interference frequency.
For at least one of the first and second approximations, the number N of beam frequencies is preferably equal to a number Ms of interference frequency choices. The range of beam frequencies can be used to determine a lower bound of effectively measurable path length differences between the object and reference beams, and an average increment between adjacent beam frequencies can be used to determine a range of unambiguous path length differences. The lower bound of path length differences between object and reference beams within the unambiguous range is associated with an interference frequency of unity or less cycles of constructive and destructive interference within the range of beam frequencies. The upper bound of path length differences within the unambiguous range is associated with an interference frequency of N/2 cycles of constructive and destructive interference within the range of beam frequencies.
For measuring surface topographies, interferometric data is recorded for a plurality of corresponding areas appearing in each of the N interference patterns. The interferometric data for each of the corresponding areas cycles through conditions of constructive and destructive interference with the variation in the beam frequencies. A plurality of first approximations of interference frequencies are made corresponding to the number of interference cycles the interferometric data for the corresponding areas undergo throughout the range of beam frequencies. The individual bounds of the first approximations are determined. A plurality of second approximations of the interference frequencies are made within the individual bounds of the first approximations of the interference frequency. The second or higher approximations of the interference frequencies are then converted into measures corresponding to a path length difference between different portions of the object and reference beams that interfere within the corresponding areas of the interference patterns. The interference patterns can be recorded as overlapping images of a test object surface and a reference element surface for relating the path length differences to surface height variations at corresponding locations on the test object surface.
Finer or additional measuring stage measurements can be made by performing a third approximation of the interference frequency within the bounds of the second approximation of the interference frequency. The third or a higher approximation of the interference frequency is converted into a measure corresponding to a path length difference between portions of the object and reference beams that interfere within the corresponding area of the interference patterns.
The second or higher approximation of the interference frequency can include identifying two close approximations of the interference frequency and interpolating a closer approximation of the interference frequency from the two close approximations of the interference frequency. For example, the closer approximation can be identified at a location where a first derivative of an implied sinusoidal function has a zero value.
The invention can also be practiced as a system for deriving length information from interferometric data collected over a range of different frequencies. A frequency-scanning interferometer produces a series of interference patterns between object and reference beams over the range of different frequencies. A common location within the interference patterns discretely cycles over the range of different frequencies through conditions of constructive and destructive interference at a rate corresponding to an interference frequency. A data acquisition system acquires data samples from the common location within the series of interference patterns. A processor evaluates a first set of interference frequency samples against the data samples to obtain a first approximation of the interference frequency that matches the cycle rate of the data samples and evaluates a second set of interference frequency samples in the vicinity of the first approximation of the interference frequency against the data samples to better approximate the interference frequency that matches the cycle rate of the data samples. In addition, the processor relates the better approximated interference frequency to length differences between the object and reference beams.
The first set of interference frequency samples are preferably frequency components of a Fourier transform that are compared to determine a peak interference frequency. The Fourier frequency components of the first set of interference frequency samples are spaced apart at a first increment, and the Fourier frequency components of the second set of interference frequency samples are spaced apart at a second increment that is finer than the first increment. The Fourier frequency components of the second set of interference frequency samples encompass a frequency range approximately equal to the first increment at which the first set of interference frequency samples are spaced apart.
Preferably, the first increment is no larger than a unit interference frequency. For example, the first increment can be equal to one-half of a unit interference frequency. The processor preferably correlates at least one of the sets of the interference frequency samples with the data samples by a Fourier transform that identifies the interference frequency sample of the set that best matches the cycle rate of the data samples. Both sets of the interference frequency samples are correlated with the data samples by the Fourier transform, which identifies the interference frequency sample of each set that best matches the cycle rate of the data samples.
A plurality of common locations in the interference patterns can be evaluated for measuring surface topographies or other multi-point measurements. The data acquisition system acquires individual groups of data samples from the plurality of common locations within the series of interference patterns. The processor separately evaluates the first set of samples of the interference frequency against the individual groups of data samples to obtain first approximations of the interference frequencies that match the cycle rates of the individual groups of data samples. The processor then separately evaluates second sets of samples of the interference frequency in the vicinity of the first approximations of the interference frequency against the individual groups of data samples to better approximate the interference frequencies that match the cycle rates of the individual groups of data samples.
The same first set of samples of the interference frequency can be evaluated against the groups of data samples. However, different second sets of samples of the interference frequency are evaluated against the groups of data samples in accordance with differences between the first approximations of the interference frequency associated with the different groups of data samples. The processor relates the better approximated interference frequencies to range information between the object and reference beams for deriving topographical information about a test surface or other multiple-point information.
A third set of samples of the interference frequency can be evaluated in the vicinity of the second approximation of the interference frequency against the data samples to even better approximate the interference frequency that matches the cycle rate of the data samples. The data samples and interference frequency samples of any one of the sets are preferably arranged to optimize a fast Fourier transform.
The invention can also be practiced as a method of reducing calculations of a frequency transform for converting interferometric data into length differences between object and reference beams. The interferometric data is acquired from a plurality of interference patterns produced by the object and reference beams and distinguished by frequencies of the beams. A succession of N interference data points are extracted from corresponding portions of the interference patterns. The succession of data points cycle through conditions of constructive and destructive interference at an interference frequency related to the path length differences between the test and reference beams. A Fourier transform is constructed of the type used for evaluating frequency contributions of M Fourier samples distributed throughout Fourier frequency space to the N data points collected from the interference patterns. The Fourier transform is limited to the evaluation of less than M Fourier frequency samples similarly distributed throughout a limited portion of the Fourier frequency space. An approximation of the interference frequency is identified from among the less than M Fourier frequency samples as a measure of the path length difference between the test and reference beams.
Preferably, the Fourier transform is limited to the evaluation of no more than M/2 Fourier frequency samples similarly distributed throughout the no more than one-half of the Fourier frequency space, and the approximation of the interference frequency is identified from among the no more than M/2 Fourier frequency samples. Prior to performing the Fourier transform, a mean intensity of the data points is calculated and the calculated mean is subtracted from the data points. The operation removes an intensity bias, leaving the intensity values of the data points as a better fit for an unbiased sinusoidal curve.
For performing a multi-stage measurement, a first approximation of the interference frequency is identified from among the Fourier frequency samples limited to no more than N Fourier frequency samples and more preferably to N/2 samples. A second approximation of the interference frequency is identified from among new Fourier samples that further divide the Fourier frequency space in the vicinity of the first approximation of the interference frequency. The Fourier frequency space considered for the second approximation is preferably equal to the Fourier frequency space between the Fourier frequency samples of the first approximation. The number of such frequency samples is preferably equal to 2M/N samples.
Briefly described, the preferred embodiments of the invention provide a wavelength scanning interferometry system having means for deriving a plurality of samples of interferometric data, as for example with a system of the type shown in FIG. 1, wherein the computation of range value for the interferometric data is carried by a computer system operating in accordance with a program (software or process) for fast and accurate computation of the range value. This program provides accuracy by using a large number of Fourier samples and achieves speed by performing a systematic search for the peak value and thus computing the Fourier transform only at necessary points in the Fourier domain. This search for the peak Fourier value occurs first at low (coarse) resolution over a reduced number of Fourier samples equally over the Fourier space to provide an estimated location of the peak Fourier value and then at a high resolution search for the peak Fourier value using the full number of Fourier samples limited to the region in the Fourier space vicinity of the estimated peak Fourier value.